Objectives
This course deals with modelisation using time continous processes. The goal is to present both theoritical and pratical aspects on stochastic differentiale equations. The second part deals with numerical method to simulate stochastic processes. It is more specifically for students of Mathematic, Actuarial and quantitative finance options and Masters. It is requiered to have followed a course on theory of probability (for example the course in S8 in Ecole Centrale de Lyon)
Keywords
Brownian Motion, Martingales, Ito calculus, Numerical simulations, Monte Carlo Markov chain methods
Programme
Mouvement Brownien, intégrale d’Ito processus de diffusion, EDS- Méthodes de Monte Carlo, important sampling, réduction de variance
- Simulation de processus aléatoires (EDS, quantification, autres ?)
- MCMC, Metropolis Hasting et autres Gibbs
Learning Outcomes
- Modelisation with a stochastic differential equation
- Ito calculus
- Approximation of a diffusion. Practical aspects
- Gibbs algorithme or annealing method; Practical aspects
Assesment
Final mark =60% Knowledge + 40% Know-how Knowledge= 100% final exam Know-how= 100% continuous assessment
Specific concerning Master students